Smith Jnr was told by Obama: "I can neither confirm nor deny the existence of extraterrestrials. But I can tell you if there had been a top-secret meeting and if there would have had to have been a discussion about it, it would have taken place in this room."
It's interesting that this anecdote comes from Smith, as it's one of his films that provides the most famous example of a Hollywood president dealing with an alien invasion.
It came in 1996's ludicrous Independence Day in which Bill Pullman's President Whitmore not only gives a gee-up talk to a ragtag crew of pilots before they go and attack an alien mothership, but actually flies one of the fighter jets.
This is explained by the President being a fighter pilot from the first Gulf War. This is ridiculous for many reasons, not least because Whitmore's rise from fighter pilot to the West Wing must have taken a maximum of five years.
Much less belligerent, but a great deal cooler was another 1996 president - Jack Nicholson's Jimmy Dale in Tim Burton's B-movie pastiche Mars Attacks!
Nicholson plays Dale as a dovish leader trying to prevent outright war with the invading Martians. Something that culminates with him asking their leader, "Why can't we all just get along?" before being impaled by a wriggling alien hand.
Zero points for alien prevention but some at least for the idea of Jack Nicholson as Potus.
Others fare equally badly. In Superman II, after Kryptonian hardbaskets Zod, Ursa and Non make their way to the White House, the President - played by EG Marshall - is forced to "kneel before Zod" and surrender on behalf of the "entire planet". Which is somewhat presumptuous as well as cowardly.
Other modern presidents to take on aliens head-first include Leslie Nielsen's President Baxter Harris in the lamentable Scary Movie franchise.
In SM4 Harris misses an invasion because - subtle satire alert! - he's busy reading a children's book entitled My Pet Duck.
Despite the golden age of alien films being the 50s, few of that era's classics, such as Don Siegel's Invasion of the Bodysnatchers and original The Day The Earth Stood Still - actually feature the President himself, perhaps out of respect for the office.
Weirdly, by the time of the Clinton administration, the President was getting speared by an alien hand.
Whoever wins in November, whether Obama or Romney, it's rather unlikely their alien-handling capabilities will be tested.
What might be more instructive is how alien-fighting presidents are represented in Hollywood in the future.
But - put it this way - can you imagine a proxy Romney strapping in to a fighter jet?
- The Independent